I  describe very briefly the role of Li and cobalt oxide in LiCoO2 as below , but a detailed description is given in:

Chem. Rev. 2010, 110, 1278–1319[ PLS. LOOK IN PP-1287-89]

[ LiCoO2] has the presence of a spinel Co3O4[CoO+Co2O3] in quantities smaller than 2%.[w/w]. When the cut off voltage reaches[ ideal=4.2V but would start at 3.85V],i.e. the battery is going to stop as there is going to be no more availability of electrons because the following half cell reaction is about to stop:

Li(s)------ Li(+)+e---------[1]

Then Co3O4 present in LiCoO2 comes to its rescue.

Then following half sell reaction takes place and the electrons become available again and the battery continues to work WITHOUT ANY VISIBLE CHANGE IN OVERALL STRUCTURE of LiCoO2 because there is simple conversion of Co(III) to Co(II) which is already present in the spinel[ Co3O4]

Co(III) [Co2O3 of Co3O4]----Co(II)[ CoOof Co3O4]+e---; E^0= 1.82V

[ Electrons become available]

In general, it is a question of the thermodynamics - which phase is thermodynamically favoured? If the Li content increases, the most stable phase may change accordingly, giving rise for new and sometimes even unextected structures. There are several groups that calculate and optimize those structures by means of density functional techniques or molecular dynamics calculations, see e.g. the review in:

Chem. Soc. Rev. 43 (2014) 185-204. DOI: 10.1039/C3CS60199D

This way, new structures may be predicted "from the scratch". Hope this helped, Dirk